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Home » Electronic Components » Calculating Filter Capacitor for Smoothing Ripple

Calculating Filter Capacitor for Smoothing Ripple

Last Updated on December 1, 2020 by Swagatam 45 Comments

In the previous article we learned about ripple factor in power supply circuits, here we continue and evaluate the formula for calculating ripple current, and consequently the filter capacitor value for eliminating the ripple content in the DC output.

The previous post explained how a DC content after rectification may carry the maximum possible  amount of ripple voltage, and how it may be reduced significantly by using a smoothing capacitor.

Although the final ripple content which is the difference between the peak value and the minimum value of the smoothed DC, never seem to eliminate completely, and directly relies on the load current.

In other words if the load is relatively higher, the capacitor begins losing its ability to compensate or correct the ripple factor.

Standard Formula for Calculating Filter Capacitor

In the following section we will try to evaluate the formula for calculating filter capacitor in power supply circuits for ensuring minimum ripple at the output (depending on the connected load current spec).

C = I / (2 x f x Vpp)

where I = load current

f = input frequency of AC

Vpp = the minimum ripple (the peak to peak voltage after smoothing) that may be allowable or OK for the user, because practically it's never feasible to make this zero, as that would demand an unworkable, non-viable monstrous capacitor value, probably not feasible for anybody to implement.

waveform after rectification

Let's try to understand the relation between load current, ripple and the optimal capacitor value from the following evaluation.

Relation Between Load Current, Ripple, and Capacitor Value

In the mentioned formula we can see that the ripple and the capacitance are inversely proportional, meaning if the ripple needs to be minimum, the capacitor value needs to increase and vice versa.

Suppose we agree to a Vpp value that's, say 1V, to be present in the final DC content after smoothing, then the capacitor value may be calculated as shown below:

Example:

C = I / 2 x f x Vpp (assuming f = 100Hz and load current requirement as 2amp))

Vpp should be ideally always a one because expecting lower values can demand huge unpracticable capacitors values, so "1" Vpp can be taken as a reasonable value.

Solving the above Formula we get:

C = I / (2 x f x Vpp)

= 2 / (2 x 100 x 1) = 2 / 200

= 0.01 Farads or 10,000uF (1Farad = 1000000 uF)

Thus, the above formula clearly shows how the required filter capacitor may be calculated with respect to the load current and the minimum allowable ripple current in the DC component.

By referring to the above solved example, one may try varying the load current, and/or the allowable ripple current and easily evaluate the filter capacitor value accordingly for ensuring an optimal or the intended smoothing of the rectified DC in a given power supply circuit.

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About Swagatam

I am an electronic engineer (dipIETE ), hobbyist, inventor, schematic/PCB designer, manufacturer. I am also the founder of the website: https://www.homemade-circuits.com/, where I love sharing my innovative circuit ideas and tutorials.
If you have any circuit related query, you may interact through comments, I'll be most happy to help!

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  1. VIJAY AJ says

    Nice post sir really useful information.

    Reply
    • Swagatam says

      thanks Vijay, I am glad you liked it….

      Reply
    • Alamgir Hossain says

      nice post sir.really helpful….. thanks sir

      Reply
    • Swagatam says

      It's my pleasure Alamgir

      Reply
  2. VIJAY AJ says

    Sir, I have seen more number of inverter circuits on your site. Can u suggest the circuit which should produce an exact sinewave as same grid supply.

    Reply
    • Swagatam says

      Vijay, trying to acquire an analogue sinewave replication can make an inverter inefficient, that's why all inverers rely on PWM which is much suited with digital inverters and are able to deliver max efficiency… and also a waveform quite similar to a pure sine wave.

      Reply
    • VIJAY AJ says

      Sir I planned to design an inverter for my home which should light up 3,20 watt cfl bulb and also for mobile charging.hence I assumed that my total watt requirement is not more than 100watt.please suggest any circuit based on my requirement and say the information about the battery that I need to use for operating an inverter for 5 hours.

      Reply
    • Swagatam says

      Vijay, you can try the following circuit:

      https://www.homemade-circuits.com/2012/09/mini-50-watt-mosfet-inverter-circuit.html

      the battery should be rated at at least 12V, 75 AH

      the inverter is capable of handling up to 200 watts if the trafo is appropriately rated

      Reply
  3. Raveesh H P says

    Dear Sir,

    For SMPS (step down) out put capacitor calculation whether we have to take switching frequency as "f" in the formula? please clarify

    Reply
    • Swagatam says

      Dear Raveesh, in SMPS, the waveform is rectangle or square and also the duty cycle factor is present…so may be the "F" could be differently expressed here in terms of duty cycle %….not much sure about it right now…

      Reply
  4. VIJAY AJ says

    Sir output of my transformer after rectification is 11.9v I want to charge my 12v battery please suggett the capacitor rating I want to use here to charge my battery please reply fast

    Reply
    • Swagatam says

      Vijay, if you are interested t calculate the exact value of the capacitor then you'll need to evaluate charging current first, which can be found by dividing the AH of your battery with 10.

      In general you can simply use the highest value capacitor that may be feasible for you.

      Reply
  5. Paul says

    A very good post that I have learnt a lot. Please how do we measure/calculate/obtain the Vpp?

    Reply
    • Swag says

      I am glad you liked!!

      Vpp is the final ripple that may appear with the DC after rectification, and it is supposed to be zero ideally, but in the practical world a zero ripple cannot be possible, and moreover that would demand a huge filter capacitor…therefore we assume this value to be around “1” for all filter capacitor calculations

      Reply
  6. Paul says

    Thank you so much for your clarification. You have helped so much.

    Reply
    • Swag says

      You are welcome!!

      Reply
  7. jax says

    very good post and site
    and about calculating filter capacitor voltage what’s your idea?

    Reply
    • Swag says

      Thank you Jack!

      Reply
  8. Deepak lodha says

    sir, your circuit is great but i have questions to you …how did you do ?

    Reply
  9. Ram Singh says

    C = I / 2 x f x Vpp

    = 2 / 2 x 100 x 1

    = 0.01 Farads or 10,000uF (1Farad = 1000000 uF)
    Where did you get the decimal point from?
    I’m trying to figure out the size of capacitor for a kbpc3508 diode bridge rectifier.

    Reply
    • Swagatam says

      C = I / (2 x f x Vpp)

      = 2 / (2 x 100 x 1)
      = 2 / 200
      = 0.01 Farads

      Reply
      • Matheo says

        0.01 Farads is 10000uF and not 10,000uF or i am wrong here?

        Reply
  10. Matheo Koning says

    I do not understand. So you should have a capacitor of 20000uf in the example above?

    Reply
  11. Pedro says

    I am trying to build a 250 to 300 volt 5 to 6 amp power supply or battery charger to charge the battery on my 03 Prius thanks if you can help

    Reply
    • Swagatam says

      You can build the auto cut off circuit by referring to the following circuit:

      https://www.homemade-circuits.com/high-voltage-360v-battery-charger/

      Reply
  12. Shaurya Gupta says

    Hello, I have a BLDC motor controller rated for 22.2V and 50A, I need to put the input power filter capacitors on them. how should I proceed? Motor operating voltage is 22 volts, peak current draw is 40A.

    Reply
    • Swagatam says

      You can use 3 capacitors, join their each end in common, and connect the other 3 ends of the capacitors with the 3 wires of the BLDC motor.

      Reply
  13. david tanguay says

    how would you go about solving this problem?
    A 60 V peak full-wave rectified voltage is applied to a capacitor-input filter. If f = 49 Hz, R = 9 kΩ, and C = 44 μF, the ripple voltage is ………

    Reply
  14. Ali mowahed says

    Hello Sir,
    I am trying to get DC power supply to run a Treadmill motor. It is 3HP, 100V 23 A motor.
    I am using an SCR AC power supply and got a full bridge rectifier. The motor runs. But there is that hum. I can not for the life of me can understand what rating of smoothig capacitor I should use to soften the hum. I assume I need to use an electrolyte capacitor.
    Even after reading your article I still don’t get what voltage and what capacitance I need. Also I don’t mind using multiple capacitor and or combined with resistor or whatever it takes to do it right. I have plenty capacitors and resistors or what have you. I appreciate any help you can throw my away. And thank you for everything you do.

    Reply
    • Swagatam says

      Hello Ali, voltage of a capacitor indicates the maximum voltage that it can handle, and exceeding that voltage will cause the capacitor to burst….it has nothing to do with the microfarad value of the capacitor or the smoothing level of the capacitor. If your supply is 100V then the voltage of the capacitor can be 150V to be perfectly safe.

      If your 100V DC is coming from a bridge rectifier then you can connect the smoothing capacitor directly across the +/- supply lines, no resistors will be required.

      You can try 500uF/150V or 1000uF/150V and this will stop the humming sound for sure. The capacitor can be electrolytic or non-electrolytic it does not matter.
      Calculating the capacitor is not required, you can randomly go on increasing the value until you find the humming sound completely gone.

      Reply
      • Ali mowahed says

        I should have mentioned that I used a 1000uf, 200V electrolyte cap, + to the arrowhead side of the rectifier, parallel to the motor and rectifier and in between them, it got hot pretty good. In fact it tripped the breaker on the recepticle. I assume that is how it is wired, its’ positive to the arrow head side of the full bridge rectifier and negative on its tail end. Unless I had it wrong. Someone said if I had it backwards it won’t work… whatever was meant by that.
        Should I use a capacitor from Microwave oven, 1 MF and 1000V?
        Thanks in advance.

        Reply
        • Ali mowahed says

          That is 1Farad on the microwave cap oven, not 1MF. 🙂

          Reply
        • Swagatam says

          Yes the capacitor must be connected across the bridge rectifier output, with the positive of the capacitor going to the cathodes of the bridge diode.
          1 Farad is huge and should be enough to cancel the ripple voltage effectively.

          Reply
  15. Ali mowahed says

    Hello, I was going to edit my previous comment/post but looks like it is not possible. So this a follow up.
    When I used your formula the capacitance I need is 160,000 uf. That is a lot. I have never seen an electrolyte capacitor with such rating. The most, the highest rating electrolyte capacitor I have seen is 4500 uf and something like 220volts.
    If that is what is needed, that is a lot of capacitors.

    Reply
    • Swagatam says

      The calculation will provide the most ideal value, which is actually not required in real life experiments, since slight bit of ripple is always acceptable.
      4500uF/220V is a huge value and should be enough to completely stop the humming sound.

      Reply
      • Ali mowahed says

        I had that electrolyte capacitor wrong in terms of polarity. It is a good thing it did’t explode. Today I installed one correctly 470uf, 200V. I noticed it didn’t make much difference. Someone on youtube was saying that the ferrite thing he used with wires looped in it between the rectifier and the motor helped a lot more than using capacitor. I am thinking of using that ferrite along with a choke, if that makes any difference. Also the AC voltage regulator has 500K potentiameter. I am thinking of installing a 100K, because I have to turn the potentiameter more than half way for the motor to even turn and the capacitor made it even worse and had to turn the knob even more.

        Reply
        • Swagatam says

          Thanks for updating the info…you can definitely try those modifications, hope it solves the problem!

          Reply
  16. Larry Ball says

    Hello Swagatam

    Do you work in the world of vacuum tubes(circuits)?

    Thank You
    Larry
    Weastminster Colorado

    Reply
    • Swagatam says

      Hello Larry,

      Sorry, I do not have any ideas regarding how vaccum tubes work.

      Reply
  17. Jennifer Isaac says

    Sir,
    I am designing a current source inverter where a capacitor is introduced in the input DC side. This capacitor has to provide the 100hz ripple that is present at the output. What would be the design if this capacitor??

    Reply
    • Swagatam says

      Hello Jennifer, I have not yet investigated the current source inverter in details, therefore I am not well versed with this concept so far!

      Reply
  18. Lawrence Sprung says

    Hi, thank you for the very clear and useful information. I assume that 1 volt of ripple means that the peak v drops down by 1v. Example: if I am supplying the load with 120v then the ripple will be 120 peak down to 119 and up to 120 etc. Is this correct?
    Also, the use of anode and cathode are confusing. I looked it up online and one thing said cathode is the negative terminal and another said it is the positive. Because of the danger of connecting an electrolytic capacitor backward, can you tell me with just positive or negative. Example: my bridge diode is marked with a + and – and the electrolytic capacitor also has + and – I understand that I connect the capacitor in parallel between the diode and the load (a dc motor) So, do I connect the + terminal of the capacitor to the wire connected to the + terminal of the diode? or to the negative?

    Reply
    • Swagatam says

      Hi, thanks, regarding the ripple voltage your understanding is correct.

      Cathode, anode terms are used for diodes and LEDs…anode refers to the terminal which accepts the positive voltage…and cathode refers to the terminal which is connected towards the negative of the supply. For electrolytic capacitors we always use the term negative/positive.
      Yes the + terminal of your capacitor will go to the + supply line.

      Reply
  19. Jeffrey Bobier Siapno says

    Calculate the C-filter capacitance which will lead to a 3.5% ripple when the load is 112 mA while the input to the filter is 21Vpeak? Show your solution.

    Can you help me how to solve this

    Reply
    • Swagatam says

      Looks difficult to me since the ripple is in percentage and a load current is involved…all these will require different sets of formulas to solve.

      Reply

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